SOLUTION: Hi tutors, please help with the following math problem. Thank you very much. Jack and Mark have 49 beads. Mark and Ben have 37 beads. Jack and Ben have 60 beads. How many beads

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Question 473285: Hi tutors, please help with the following math problem. Thank you very much.
Jack and Mark have 49 beads. Mark and Ben have 37 beads. Jack and Ben have 60 beads. How many beads does each of them have and the sum of all?
I tried by adding 49 + 60 then minus 37 and divide 3, which I got 24. After that, i am stuck as I couldn't figure out how many does each boy have. I totaled up the numbers to be 74 but the answer should be 73.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let J = # of beads Jack has, M = # of beads Mark has, and B = # of beads Ben has


Since "Jack and Mark have 49 beads", we know that J%2BM=49. Solve for M to get M=49-J


Because "Mark and Ben have 37 beads", we know that M%2BB=37. Plug in M=49-J to get %2849-J%29%2BB=37. Now solve for B to get B=37-49%2BJ ---> B=-12%2BJ


Since "Jack and Ben have 60 beads", we see that J%2BB=60. Plug in B=-12%2BJ to get J%2B%28-12%2BJ%29=60, which will simplify to 2J-12=60


Now solve for J


2J-12=60


2J=60%2B12


2J=72


J=72%2F2


J=36


So Jack has 36 beads.


So Mark has M=49-J=49-36=13 beads


So Ben has B=-12%2BJ=-12%2B36=24 beads


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Answer:

Jack has 36 beads, Mark has 13 beads, and Ben has 24 beads.


In total, they have 36+13+24 = 73 beads

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Jack and Mark have 49 beads.
Mark and Ben have 37 beads.
Jack and Ben have 60 beads.
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Equations:
0 + j + m = 49
b + 0 + m = 37
b + j + 0 = 60
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How many beads does each of them have and the sum of all?
----
I used a matrix method to get:
b = 24
j = 36
m = 13
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# of beads = 24+36+13 = 73
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Cheers,
Stan H.